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Valve ban advertising-based business models on Steam, no forced adverts like in mobile games
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I think what they dont allow is having a store in their store. You can easily install a third party store on Android at least but you cant do it through googles store. They dont care if you do, they just wont help you do it. AFAIK, theres legislation in the works to prevent this since not offering third party stores is monopolistic akin to Internet Explorer being pre installed on windows.
Play services is not the same as Andoird. Manufacturers can decide what goes.